Deuteron Breakup Threshold Research Articles

Matrix Elements for Low-Energyp−dRadiative Capture

The radiative capture reaction p 1 d ! 3He 1 g has been the focus of many experimental and theoretical studies over the past 20 years, and during this time experiments with polarized protons and deuterons have come to be fairly common. Initially, the interest in polarization experiments arose in part from the observation that the “tensor analyzing powers” for p-d capture are sensitive to D-state components in the 3He wave function [1–4]. Additionally, it was known that measurements of the proton analyzing power and the deuteron vector analyzing power are sensitive to M1 transitions [5,6] which can be influenced by meson exchange processes and non-nucleonic degrees of freedom. Recently, the focus of the work in this field has expanded somewhat as theorists continue to make progress in developing techniques for performing exact quantum calculations in few-body systems. Within just the last few years we have seen publication of the first calculations [7] of p-d radiative capture which incorporate both realistic NN interactions and a correct treatment of Coulomb forces. In view of this new capability, one may now view p-d capture experiments as a means for testing, in a more general way, our understanding of the spin structure of the A ­ 3 system and of the fundamental NN interaction. The purpose of this Letter is to present a new set of measurements for p-d radiative capture at an energy just below the deuteron breakup threshold, Ec.m. ­ 2 MeV. We also describe a new method for the analysis of subthreshold capture data, which is based on Watson’s theorem [8]. This new technique has made it possible to carry out a partial-wave analysis of the data which is significantly more extensive in scope than any previous analysis of this kind for p-d capture. The value of a partial-wave analysis should be readily apparent. In this kind of analysis one determines (by fitting data) a set of parameters which specify the contributions to the reaction amplitude from the individual angular momentum states. In general, a partial-wave analysis provides insight about the details of the reaction process (see, for example, Ref. [9]), and, in addition, makes it possible to compare theory and experiment at a more fundamental level.

Proton-Deuteron Elastic Scattering above the Deuteron Breakup

The complex Kohn variational principle and the (correlated) hyperspherical harmonics method are applied to study the proton-deuteron elastic scattering at energies above the deuteron breakup threshold. Results for the elastic cross section and various elastic polarization observables have been obtained by fully taking into account the long-range effect of the Coulomb interaction and using a realistic nucleon-nucleon interaction model. Detailed comparison between the theoretical predictions and the accurate and abundant proton-deuteron experimental data can now be performed.

Benchmark calculations for polarization observables in three-nucleon scattering

High precision benchmark calculations for phase shifts and mixing parameters as well as observables in elastic neutron-deuteron scattering below the deuteron breakup threshold are presented using a realistic nucleon-nucleon potential. Two totally different methods, one using a variational principle in configuration space and the other solving the Faddeev equations in momentum space, are used and compared to each other. The agreement achieved in phase shifts and mixing parameters as well as in the polarization observables is excellent. The extreme sensitivity of the vector analyzing power A{sub y} to small changes of the phase shifts and mixing parameters is pointed out. thinsp {copyright} {ital 1998} {ital The American Physical Society}

Variational study of 3N scattering

A variational method is used to describe scattering states in the three-nucleon system. Using appropriate boundary conditions, the method can be applied to energis above the deuteron breakup threshold. The inclusion of long range potentials as the Coulomb interaction does not cause additional difficulties. Numerical results are given for central spin dependent forces.

An energy-dependent phase shift analysis of low-energy proton-deuteron elastic scattering

An energy dependent phase shift analysis of p+d elastic scattering below the deuteron breakup threshold has been conducted. The phases are fit directly to the data with a Monte Carlo Markov Chain algorithm after being sampled from a parameter space which is constrained to satisfy the Coulomb-modified effective range expansion. The mixing parameters are required to obey analyticity constraints. The overall fit in the preliminary analysis reported here was satisfactory, giving a χ 2/datum of about 2.5. The analysis indicates the existence of a singularity in the spin-doublet S-wave effective range function. The inferred value of the quartet S-wave scattering length is in excellent quantitative agreement with theoretical predictions. Small changes to the theoretical P-wave phase shifts and somewhat larger changes to the theoretical J = 1 2 mixing parameters are required to reproduce the p+d data.

N-dscattering above the deuteron breakup threshold

The complex Kohn variational principle and the (correlated) hyperspherical harmonics technique are applied to study $N$-$d$ scattering above the deuteron breakup threshold. The configuration with three outgoing nucleons is explicitly taken into account by solving a set of differential equations with outgoing boundary conditions. A convenient procedure is used to obtain the correct boundary conditions at values of the hyperradius of $\ensuremath{\approx}100$ fm. The inclusion of the Coulomb potential is straightforward and does not give additional difficulties. Numerical results have been obtained for a simple $s$-wave central potential. They are in nice agreement with the benchmarks produced by different groups using the Faddeev technique. Comparisons are also done with experimental elastic $N$-$d$ cross section at several energies.

Critical comparison of experimental data and theoretical predictions for N-d scattering below the breakup threshold

The theoretical approaches for studying N-d processes using realistic, semi-phenomenological NN potentials have matured considerably during the last few years. Accurate calculations of scattering observables are now feasible. Recently, high-quality measurements of N-d scattering at energies below the deuteron breakup threshold became available. Therefore, a detailed comparison between theory and experimental data can now be performed. In this paper the various sets of experimental data for the N-d differential cross section, and the vector and tensor analyzing powers are examined in a critical way in the incident nucleon energy range from 1 to 3 MeV. In order to identify possible inadequacies of the interaction models adopted, phase-shift analyses were performed and compared to the theoretical parameters.

Analyzing powers of p+d scattering below the deuteron breakup threshold.

All the vector and tensor analyzing powers of the p+d scattering have been measured at ${\mathit{E}}_{\mathit{p}}^{\mathrm{lab}}$=2.5 MeV (${\mathit{E}}_{\mathit{d}}^{\mathrm{lab}}$=5 MeV), where a calculation of the three-nucleon scattering state with an improved treatment of Coulomb force has become available. Measurements have also been made at energies below and slightly above the deuteron breakup threshold at ${\mathit{E}}_{\mathit{p}}^{\mathrm{lab}}$ = 3.34 MeV. The experimental data have small statistical errors ranging from \ifmmode\pm\else\textpm\fi{}0.0004 to \ifmmode\pm\else\textpm\fi{}0.0008, and the uncertainties in the scale are less than 1%. The present data together with our previous data on the cross section are compared with several Faddeev calculations based on a separable-form nucleon-nucleon potential or on a realistic potential with Coulomb force being treated nearly correctly or approximately. Disagreements between the calculations and the experiment are found not only in the cross section and the vector analyzing powers ${\mathit{A}}_{\mathit{y}}$ and ${\mathit{iT}}_{11}$ but also in the tensor analyzing powers ${\mathit{T}}_{21}$ and ${\mathit{T}}_{22}$.

Effects of the three-nucleon forces due to pi and rho meson exchanges in the three-nucleon continuum.

Using the Bonn B nucleon-nucleon potential and the Tucson-Melbourne family of \ensuremath{\pi}-\ensuremath{\pi}, \ensuremath{\pi}-\ensuremath{\rho}, and \ensuremath{\rho}-\ensuremath{\rho} three-nucleon forces we solved the 3N Faddeev equation below and above the deuteron breakup threshold. For different elastic scattering and breakup observables we looked for the effects caused by adding consecutively the above 3N forces. The largest effects were found for the \ensuremath{\pi}-\ensuremath{\pi} three-nucleon force. The influence of \ensuremath{\pi}-\ensuremath{\rho} exchange was generally found to be smaller than \ensuremath{\pi}-\ensuremath{\pi} and it acts in opposite direction. The effect of the \ensuremath{\rho}-\ensuremath{\rho} three-nucleon force was found to be always negligible. Adding \ensuremath{\pi}-\ensuremath{\rho} and \ensuremath{\rho}-\ensuremath{\rho} three-nucleon forces does not explain the analyzing power puzzle in the low energy nucleon-deuteron elastic scattering.

Analyzing power in neutron-deuteron elastic scattering at Elabn=3 MeV.

A measurement of the analyzing power ${\mathit{A}}_{\mathit{y}}$(\ensuremath{\theta}) in neutron-deuteron (n-d) elastic scattering below the deuteron breakup threshold is described, including a detailed discussion of the experimental apparatus and the treatment of systematic errors. The data provide a precise test of Faddeev calculations of the three-nucleon system and of the nucleon-nucleon interaction models used as inputs to these calculations. ${\mathit{A}}_{\mathit{y}}$ was measured at six angles from 44.5 \ifmmode^\circ\else\textdegree\fi{} c.m. to 145.7 \ifmmode^\circ\else\textdegree\fi{} c.m. to a precision of (7--13)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$. Polarized neutrons, produced by the $^{3}\mathrm{H}$(p\ensuremath{\rightarrow},n\ensuremath{\rightarrow}${)}^{3}$He reaction, were incident upon the target, a deuterated organic scintillator. Scattered neutrons were detected in fast coincidence with the recoil deuterons in the target. A computer simulation of the experiment was used to compensate for a number of systematic errors. Particularly important were corrections for neutron multiple scattering, accidental coincidences, and finite geometry effects. The ${\mathit{A}}_{\mathit{y}}$ data have a 2.2% scale factor uncertainty associated with uncertainty in the polarization of the incident neutron beam. The incident neutron polarization was measured in a separate experiment using n${\mathrm{\ensuremath{-}}}^{4}$He scattering from a liquid helium scintillator. The neutron polarization measurement also yielded an improved value for the polarization transfer coefficient [${\mathit{K}}_{\mathit{y}}^{\mathit{y}}$(${0}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$)=0.650\ifmmode\pm\else\textpm\fi{}0.019] in the $^{3}\mathrm{H}$(p\ensuremath{\rightarrow},n\ensuremath{\rightarrow}${)}^{3}$He reaction at ${\mathit{E}}_{\mathrm{lab}}^{\mathit{p}}$=3.80 MeV. A comparison of the ${\mathit{A}}_{\mathit{y}}$ data to Faddeev calculations shows that the discrepancy in ${\mathit{A}}_{\mathit{y}}$ observed previously at higher energies continues below the breakup threshold. A comparsion of the ${\mathit{A}}_{\mathit{y}}$ data to a recent phase shift analysis of proton-deuteron (p-d) scattering indicates that observed differences between n-d and p-d analyzing powers are only partially explained by Coulomb effects.

Analyzing power in nd elastic scattering at Enlab=3 MeV. Measurement and calculation

A precision measurement of the neutron-deuteron analyzing power below the deuteron breakup threshold is presented and compared to rigorous 3N calculations based on the Argonne AV 14, Bonn B, Nijmegen and Paris potentials. A significant discrepancy between theory and experiment is found, similar to that seen at higher energies. A modification of the NN interaction which includes charge independence breaking in the 3P J partial waves is discussed which improves the description of the data at all energies.

Complex local potential by Marchenko inversion of partly real and partly complex phase shift.

By using the (in general complex) phase shifts for elastic neutron-deuteron scattering in the quartet channel, calculated by means of the exact few-body theory, as input in the fixed-{ital l} inverse scattering theory of Marchenko, we construct equivalent local two-body potentials. The latter, though being complex and energy independent, nevertheless reproduce the input phase shifts, which are real below and complex above the deuteron breakup threshold, to a high accuracy. It is even more remarkable that the scattering wave functions (with real boundary conditions) for energies in the elastic regime, calculated with these potentials, are real outside the range of the force, and to a very good approximation real also in the interior region.

Three-body calculation of deuteron-nucleus coulomb field interaction

Abstract A consistent theory is developed for the calculation of a potential of the interaction of a deuteron with the Coulomb field of a nucleus. Its characteristics at large distances are studied. The explicit form for the deuteron-nucleus interaction at the deuteron breakup threshold is given. In the limit of a small energy for relative deuteron-nucleus motion a simple potential containing off the energy shell effects is derived and the physical nature of its constants are explained. The accuracy of a transition to polarization interaction is established. A new formula for the calculation of electric dipole polarizability for the two-particle system is obtained.

Exchange currents in pion-induced deuteron breakup

Exchange-current contributions in pion-nucleus reactions are in general small due to the nature of the effective pion-nucleus interaction. The reactionπ−d→π−np near the deuteron breakup threshold provides an exception. The isovector exchange current should give the largest contribution to this cross section for momentum transfer values between3 and 4 fm−1

The Efimov effect in neutron-deuteron elastic scattering near the deuteron breakup threshold

A phase shifts analysis for neutron-deuteron and proton-deuteron scattering is made at three-body threshold using the Faddeev equation in configuration space.

Elastic neutron-deuteron doublet scattering near the deuteron breakup threshold

The anomalous behavior, as suggested by Efimov, in the doublet n-d scattering near the deuteron breakup threshold is investigated by computing coupled integral equation using s-wave separable potentials.

On the irregularity in doublet neutron-deuteron elastic scattering near the deuteron breakup threshold

A “rounded-step” irregularity is calculated to be present in doublet neutron-deuteron elastic scattering near the deuteron breakup threshold.

Analyse de la diffusion élastique neutron deuton à basse énergie

The results of an effective-range analysis of elastic n-d scattering below the deuteron break-up threshold are given. Total spin and orbital angular momentum are supposed to be conserved and J-degeneracy is admitted. The S-, P- and D-states only are taken into account. No confirmation of the pole of Van Oers and Seagrave in the efiective-range function of the 2S state has been obtained.

The [formula omitted] reaction at the breakup threshold

Gamma-ray yields with 2 H(p, γ) 3 He reaction have been measured in the region of the deuteron breakup threshold. The excitation function does not display any cross section anomaly of significance at the breakup threshold.